1, The plural "sabbasin" is not odd at all; the plural is about
as common as the singular to refer to a single sabbath day, at
least from 3rd century BCE on, including Plutarch and Philo and
Josephus. "Why the plural?" Because that's the way they said
it. In English, we don't talk this way -- but then, we aren't
talking Greek, are we? Bauer gives you plenty of info on this.

2. "TI `HMIN KAI SOI?" isn't stupid. The phrase is used in
classical Greek, in singular and plural for each pronoun, and
means "What do we have in common?"; it is used a lot in
Hellenistic texts, and it also is in LXX as a direct translation
of the Hebrew which is literally the same. In John 2:4 Jesus
says it to his mother. It's all part of learning Greek: Greek is
not a code for English, so matching words one-to-one isn't how to
understand the Greek language.

3. I'm not sure where your problem lies. To give the
"schoolboy translation" for the aorist participles, it would run:
"And after the unclean spirit had convulsed him, and after it had
cried out with a great cry, it left him." Or. also "schoolboy
participle," "The unclean spirit having convulsed him, and
having cried out with a great cry, it left him." Such a
translation is too wooden, and lays too much of a burden on the
notion of relative temporality for the aorist participle (see
Moule's _Idiom Book_ discussion of it, where he says it works
more often than it should!); but it surely allows the "kai...kai"
to make perfect sense. If your question is, Does Mark mean that
the convulsion and the cry were simultaneous? the answer is that
we can't tell from this sentence.

4. The three adverbs in a row (1:35, PRWI ENNUCA LIAN) are a
bit unusual, probably due to Mark's liking to say things more of
less twice; but the meaning is obvious. Early in the morning,
still dark, very much so -- Either: Very early in the morning,
while still dark (likelier), or Early in the morning, while it
was still very dark (slightly less likely).

But surely your own professors of Greek at the GTU could answer
these questions.